Hi, you have to change it also in the pass. Please get in touch with customer service for this:

Submit a request – Eurail Knowledge Base

Do you travel soon?

Hi, thank you so much for such a quick response. 
Yes, I will start my journey next week and I need to make a reservation for a train from Brussels to London. Is it possible to do it before the country of residence is changed or shall I wait?

I have already contacted the support service. Thanks for the link! 

Have a nice day:)

Next week? Eurostar is very busy and may well already be booked out or passholders.

https://www.b-europe.com/EN/Booking/Pass#TravelWish for passholder spaces, use cover number generator

Hello, I am sorry to hear of the incorrect country of residence. Unfortunately, our customer service team can't change the country of residence on a pass. This is a fixed detail and the only way to change this is to request a pass exchange. It might be useful to point out that your current pass needs to be valid and inactive to be eligible for a regular exchange. To facilitate a pass exchange, please purchase a new pass with the correct country of residence and get in touch with customer service with your old and new order number. We will then refund the old pass. We retain a €15 processing fee per pass. This process is free for travelers with PLUS. Certain promotional passes might not be eligible for an exchange/refund. You can usually see eligibility on the invoice that you received in the payment confirmation email. I hope this helps! :)